Two identical firms compete as a Cournot duopoly. The inverse market demand they face is P...

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Two identical firms compete as a Cournot duopoly. The inverse market demand they face is P...

Two identical firms compete as a Cournot duopoly. The inverse market demand they face is P = 128 - 4Q. The cost function for each firm is C(Q) = 8Q. The price charged in this market will be: a. $32. b. $48. c. $12. d. $56.

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Answer 1

Answer #1

Option (b).

MC1 = MC2 = dC/dQ = 8

P = 128 - 4Q1 - 4Q2

For firm 1,

TR1 = P x Q1 = 128Q1 - 4Q1² - 4Q1Q2

MR1 = TR1/Q1 = 128 - 8Q1 - 4Q2

Setting MR1 = MC1,

128 - 8Q1 - 4Q2 = 8

8Q1 + 4Q2 = 120..........(1) (best response, firm 1)

For firm 2,

TR2 = P x Q2 = 128Q2 - 4Q1Q2 - 4Q2²

MR2 = TR2/Q2 = 128 - 4Q1 - 8Q2

Setting MR2 = MC2,

128 - 4Q1 - 8Q2 = 8

4Q1 + 8Q2 = 120..........(2) (best response, firm 2)

Multiplying (2) by 2,

8Q1 + 16Q2 = 240.........(3)

8Q1 + 4Q2 = 120.........(1)

(3) - (1) gives:

12Q2 = 120

Q2 = 10

Q1 = 10 [since cost function is identical for both firms, Q1 = Q2]

Q = Q1 + Q2 = 20

P = 128 - 4 x 20 = 128 - 80 = 48

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Answer 2

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